论文标题
在自旋链上的一系列交换操作的保真度
Fidelity of a sequence of SWAP operations on a spin chain
论文作者
论文摘要
我们考虑通过使用重复交换门的使用，从Heisenberg耦合的旋转链中进行旋转状态的``运输''，从两种状态之一开始-----最左边的旋转是一种，其中最左边的旋转是向下，另一个旋转是向上旋转的，其中最左边的两个旋转处于单身状态（即，它们是单身状态（即，它们又一次），以及其他所有旋转状态。更具体地说，我们``运输''在第一种情况下最左边的旋转状态，第二个情况下又是链的另一端，然后再旋转，然后再次返回。我们通过增加从基本值$ j $进行的两个旋转之间的交换耦合来完成此处的掉期操作，以$ j $ $ j_ \ text {swap} $在一个时间内$ t =π\ hbar/4j_ \ text {swap {swap} $。我们在多种情况下确定了这种操作序列的忠诚度 - 其中仅存在最近的邻居耦合，并且没有磁性偶极 - 偶极偶联或噪声（最理想的情况）（最理想的情况），我们引入了下一个neartest-neart-neart-neegr-neak-neegr-neegr-neegr-neegr-neighbor耦合，但没有其他效果，以及这些效果的效果。在最后一个情况下，假定噪声是绝对的，即，交换耦合每个都从高斯分布中绘制，仅截断为非负值。我们将保真度绘制为$ j_ \ text {swap} $的函数，以说明各种效果，即由于与其他旋转以及噪声耦合，这对我们执行交换操作的能力有害。我们的理论对于构建基于半导体的旋转量子计算机体系结构的持续实验工作应该很有用。
We consider the ``transport'' of the state of a spin across a Heisenberg-coupled spin chain via the use of repeated SWAP gates, starting with one of two states---one in which the leftmost spin is down and the others up, and one in which the leftmost two spins are in a singlet state (i.e., they are entangled), and the others are again all up. More specifically, we ``transport'' the state of the leftmost spin in the first case and the next-to-leftmost spin in the second to the other end of the chain, and then back again. We accomplish our SWAP operations here by increasing the exchange coupling between the two spins that we operate on from a base value $J$ to a larger value $J_\text{SWAP}$ for a time $t=π\hbar/4J_\text{SWAP}$. We determine the fidelity of this sequence of operations in a number of situations---one in which only nearest-neighbor coupling exists between spins and there is no magnetic dipole-dipole coupling or noise (the most ideal case), one in which we introduce next-nearest-neighbor coupling, but none of the other effects, and one in which all of these effects are present. In the last case, the noise is assumed to be quasistatic, i.e., the exchange couplings are each drawn from a Gaussian distribution, truncated to only nonnegative values. We plot the fidelity as a function of $J_\text{SWAP}$ to illustrate various effects, namely crosstalk due to coupling to other spins, as well as noise, that are detrimental to our ability to perform a SWAP operation. Our theory should be useful to the ongoing experimental efforts in building semiconductor-based spin quantum computer architectures.
